Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1404 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 1404 conjugacy classes of subgroups — too many to draw. Only its 246 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C33×#127 | C2 | semidirect |
| 2. C2×C3×#3753 | C2 | semidirect |
| 3. C3×#64083 | C2 | semidirect |
| 4. C3×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10592772 | C3 | direct (N × H) |
| 15. C32×#127 | D3 | semidirect |
| 16. C32×#127 | C2×C3 | semidirect |
| 17. C2×#3753 | C2×C3 | semidirect |
| 18. #64083 | C2×C3 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 31. C3×C3⋊(C3⋊C8) | D4 | semidirect |
| 56. C33×C4 | D8 | semidirect |
| 61. C3×#127 | C3×D3 | semidirect |
| 62. C3×#127 | C3⋊D3 | semidirect |
| 88. C3⋊(C3⋊C8) | C3×D4 | semidirect |
| 127. C32×C4 | #213 | semidirect |
| 128. C32×C4 | C3×D8 | semidirect |
| 133. #127 | C3×C3⋊D3 | semidirect |
| 135. C33 | #493 | semidirect |
| 192. C3×C4 | C3×#213 | semidirect |
| 193. C3×C4 | #3753 | semidirect |
| 197. C32 | #5073 | semidirect |
| 198. C32 | C3×#493 | semidirect |
| 224. C4 | C3×#3753 | semidirect |
| 227. C3 | C3×#5073 | semidirect |
| 228. C3 | #10592772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#127 | 2 |
| C2×C3×#3753 | 2 |
| C3×#64083 | 2 |
| C3×C4×C3⋊(C3⋊C8) | 2 |
| #10592772 | 3 |
| C3×#5073 | 3 |